Pre-Calculus (Check)

Please tell me what I'm doing wrong...

The side lengths of tops of three squares tables can be described as three consecutive integers. The combined area of the table tops is 677 sq in.

Algebraically, determine the roots of the quadratic equation. (I'll use quadratic, but if it's easier factoring or completing the square, please tell me!)

3x^2 - 6x -677 = 0

6 +- sqrt 36- 4(3)(-677)
---------------------------
6

x = 6 +-sqrt 510
------------
6
(In this step, the sixes can be removed by division, so I don't have the proper roots)

Any help is really appreciated!

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  1. If the middle table has side x, then the three squares

    (x-1)^2 + x^2 + (x+1)^2 = 677
    3x^2 + 2 = 677
    3x^2 = 675
    x^2 = 225
    x = 15

    and the tables have sides 14,15,16

    how did you come up with 3x^2-6x = 677?

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